In this paper, we first consider the stability problem for a class of stochastic quaternion-valued neural networks with time-varying delays. Next, we cannot explicitly decompose the quaternion-valued systems into equivalent real-valued systems; by using Lyapunov functional and stochastic analysis techniques, we can obtain sufficient conditions for mean-square exponential input-to-state stability of the quaternion-valued stochastic neural networks. Our results are completely new. Finally, a numerical example is given to illustrate the feasibility of our results.
In this paper, we consider a new fractional-order predator–prey model with Holling type-III functional response and stage structure. Based on the Lyapunov stability theory and by constructing a suitable Lyapunov functional, we obtain some sufficient conditions for the existence and uniqueness of positive solutions and the asymptotic stability of the positive equilibrium to the system. Finally, we give some numerical examples to illustrate the feasibility of our results.
In this paper, we are concerned with a class of quaternion-valued stochastic neural networks with time-varying delays. Firstly, we cannot explicitly decompose the quaternion-valued stochastic systems into equivalent real-valued stochastic systems; by using the Banach fixed point theorem and stochastic analysis techniques, we obtain some sufficient conditions for the existence of square-mean pseudo almost periodic solutions for this class of neural networks. Then, by constructing an appropriate Lyapunov functional and stochastic analysis techniques, we can also obtain sufficient conditions for square-mean exponential stability of the considered neural networks. All of these results are new. Finally, two examples are given to illustrate the effectiveness and feasibility of our main results.
<abstract><p>This paper deals with a class of fractional-order octonion-valued neural networks (FOOVNNs) with impulsive effects. Firstly, although the multiplication of octonion numbers does not satisfy the commutativity and associativity, we don't need to separate an octonion-valued system into eight real-valued systems. Secondly, by applying the appropriate Lyapunov function, and inequality techniques, we obtain the global asymptotical synchronization of FOOVNNs. Finally, we give two illustrative examples to illustrate the feasibility of the proposed method.</p></abstract>
<abstract><p>This paper proposes a class of quaternion-valued high-order Hopfield neural networks with delays. By using the non-decomposition method, non-reduced order method, analytical techniques in uniform convergence functions sequence, and constructing Lyapunov function, we obtain several sufficient conditions for the existence and global exponential synchronization of anti-periodic solutions for delayed quaternion-valued high-order Hopfield neural networks. Finally, an example and its numerical simulations are given to support the proposed approach. Our results play an important role in designing inertial neural networks.</p></abstract>
In this paper, we consider the problem of the S-asymptotically ω-periodic synchronization of fractional-order complex-valued recurrent neural networks with time delays. Firstly, we can not explicitly decompose the fractional-order complex-valued systems into equivalent fractional-order real-valued systems, by means of the contraction mapping principle and some important features of Mittag-Leffler functions, we obtain some sufficient conditions for the existence and uniqueness of S-asymptotically ω-periodic solutions for this class of neural networks. Then, by constructing an appropriate Lyapunov functional, the theory of fractional differential equation, and some inequality techniques, sufficient conditions are obtained to guarantee the global Mittag-Leffler synchronization of the drive-response systems. Finally, two examples are given to illustrate the effectiveness and feasibility of our main results.
In this paper, a class of Clifford-valued neutral-type recurrent neural networks with D operator is explored. By using non-decomposition method and the Banach fixed point theorem, we obtain several sufficient conditions for the existence of anti-periodic solutions for Clifford-valued neutral-type recurrent neural networks with D operator. By using the proof by contradiction and inequality techniques, we obtain the global exponential synchronization of anti-periodic solutions for Clifford-valued neutral-type recurrent neural networks with D operator. Finally, we give one example to illustrate the feasibility and effectiveness of main results.INDEX TERMS Clifford algebra, recurrent neural networks, synchronization, anti-periodic solutions, D operator.
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